If sin theta = 1/3 and tan theta < 0, what is the value of cos theta?

A) 2 square root 2/3

B) - 2 square root/3

C) 2 square root 2

D) - 2 square root 2

If sin Ф=1/3>0 and tan Ф<0; then Ф belongs to the second quadrant and cos Ф will be negative (cos Ф<0).

sin²Ф+cos²Ф=1

(1/3) ²+cos²Ф=1

1/9+cos²Ф=1

cos²Ф=1-1/9

cos²Ф=8/9

cos Ф=⁺₋√ (8/9) = ⁺₋2√2 / 3

We have two possible solutions.

cos Ф=2√2 / 3 This solutions is not possible, because in this case cos Ф has to be negative (cos Ф<0)

cos Ф = (-2√2) / 3 this solutions is right.

answer:B. - 2 square root 2 / 3 (or (-2√2) / 3)